(3x+4y)(2x+5y)=

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Solution for (3x+4y)(2x+5y)= equation: 


Simplifying
(3x + 4y)(2x + 5y) = 0

Multiply (3x + 4y) * (2x + 5y)
(3x * (2x + 5y) + 4y * (2x + 5y)) = 0
((2x * 3x + 5y * 3x) + 4y * (2x + 5y)) = 0

Reorder the terms:
((15xy + 6x2) + 4y * (2x + 5y)) = 0
((15xy + 6x2) + 4y * (2x + 5y)) = 0
(15xy + 6x2 + (2x * 4y + 5y * 4y)) = 0
(15xy + 6x2 + (8xy + 20y2)) = 0

Reorder the terms:
(15xy + 8xy + 6x2 + 20y2) = 0

Combine like terms: 15xy + 8xy = 23xy
(23xy + 6x2 + 20y2) = 0

Solving
23xy + 6x2 + 20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + 4y)(2x + 5y) = 0


Subproblem 1
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y

Subproblem 2
Set the factor '(2x + 5y)' equal to zero and attempt to solve:

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {-1.333333333y, -2.5y}

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